That's because, in large part, inequality starts in the crib. Rich parents can afford to spend more time and money on their kids, and that gap has only grown the past few decades. Indeed, economists Greg Duncan and Richard Murnane calculate that, between 1972 and 2006, high-income parents increased their spending on "enrichment activities" for their children by 151 percent in inflation-adjusted terms, compared to 57 percent for low-income parents.

But, of course, it's not just a matter of dollars and cents. It's also a matter of letters and words. Affluent parents talk to their kids three more hours a week on average than poor parents, which is critical during a child's formative early years. That's why, as Stanford professor Sean Reardon explains, "rich students are increasingly entering kindergarten much better prepared to succeed in school than middle-class students," and they're staying that way.

Even poor kids who do everything right don't do much better than rich kids who do everything wrong. Advantages and disadvantages, in other words, tend to perpetuate themselves. You can see that in the above chart, based on a new paper from Richard Reeves and Isabel Sawhill, presented at the Federal Reserve Bank of Boston's annual conference, which is underway.

Specifically, rich high school dropouts remain in the top about as much as poor college grads stay stuck in the bottom — 14 versus 16 percent, respectively. Not only that, but these low-income strivers are just as likely to end up in the bottom as these wealthy ne'er-do-wells. Some meritocracy.

What's going on? Well, it's all about glass floors and glass ceilings. Rich kids who can go work for the family business — and, in Canada at least, 70 percent of the sons of the top 1 percent do just that — or inherit the family estate don't need a high school diploma to get ahead. It's an extreme example of what economists call "opportunity hoarding." That includes everything from legacy college admissions to unpaid internships that let affluent parents rig the game a little more in their children's favor.

But even if they didn't, low-income kids would still have a hard time getting ahead. That's, in part, because they're targets for diploma mills that load them up with debt, but not a lot of prospects. And even if they do get a good degree, at least when it comes to black families, they're more likely to still live in impoverished neighborhoods that keep them disconnected from opportunities.

It's not quite a heads-I-win, tails-you-lose game where rich kids get better educations, yet still get ahead even if they don't—but it's close enough. And if it keeps up, the American Dream will be just that.